I Want to dedie this thread into the following questions:Does the market have a mean? If yes to approximate it? If the mean is not constant, its variable as the market changes structure to approximate it given out sample dimensions? My research to come up with the ideal version that models the expression.
From the expression I mean the http://en.wikipedia.org/wiki/Mean,not the median, that's the separator half of the distribution in case of the price the half line of the full market which for example aproximately the (alltime highest highs alltime lowest lows) /two

So because the market is ever changing, I fixed the sample size to 1440 M1 pubs which will be 1 day of data, because its likely a plausible separator between samples since the volatility distribution can also be separated by the minimal liquidity nights when the London SE and NY SE is closed.
So I chooses 1440 to be out sample size, possibly it could have been 7200 aswell that's 1 week, since there is a volatility gap between Friday afternoon and Monday morning aswell.

That I've analyzed various moving averages to locate the mean but the majority of them werent receptive to the price.Here are the classical moving averages, I always used Median Price,dont confuse it with market median, which can be (High[position] Low[position]) /2 since it reflects the market better than Close price.

These averages have PERIOD 1440, M1 pubs, MEDIAN PRICE,SHIFT 0
And by colour are the following: Yellow=Smoothed Straightforward,Blue =Simple(Arithmetic),Purple=Exponential Weighted, Red=Linear Weighted



since you can see the linear weighted is the most reactive, and not as lagging, and the smoothed is your worst,and the simple moving average is pretty far from a mean.

And I noticed these classical moving averages are as far away from a statistical mean as the sky is from the floor, so I took my abilities and coded my own moving average, and I've been experimenting with it.Set also to PERIOD 1440, and its own orange coloured, while another MA's are the same colour but set them dashed so it becomes more visible:






since you can see its much more responsive to the price, and not as much lagging.Also I'm quantifying the variance of the price around my moving average to try and gauge from the dispersion of price around it.
I assume the the variance is, the more accurately my MA measures the mean, the problem is that if I increase the size of my MA's filter then the variance declines almost to 0, and also my MA becomes identical with a PERIOD 1 moving average.

So its almost like a period 1 moving average is the mean of this market, that is, that each tick is the current mean.However this is absurd because the MA doesnt tell anything about the trend or the prejudice in the price.

So that I would need a perfect equilibrium between LAGG AND ACCURACY or Put simply the mean which the price will hover around the maximum, which is not itself (maybe not the previous price).

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